Parallel lines and transversals worksheets can help students identify the different types of angles that can be formed like corresponding angles, vertical angles, alternate interior angles, alternate exterior angles. They can utilize this knowledge of the angles formed by parallel lines and transversals to set up and solve equations for missing angles.
Benefits of Parallel Lines and Transversals Worksheets
Parallel lines and transversals worksheets can help students to learn about angles formed by parallel lines cut by a transversal. Parallel lines and transversals worksheets will help kids in solving geometry problems. Some real-life examples of parallel lines cut by a transversal are zebra crossing on the road, road and railway crossing, railway tracks with sleepers, and windscreen wipers in cars.
Printable PDFs for Parallel Lines and Transversals Worksheets
First, students will need to be able to identify angle pairs, then know the properties and relationships. Children and parents can find these math worksheets online or even download the PDF format of these exciting worksheets.
Problem 1 :
Identify the pairs of angles in the diagram. Then make a conjecture about their angle measures.
Problem 2 :
In the figure given below, let the lines l1 and l2 be parallel and m is transversal. If ∠F = 65°, find the measure of each of the remaining angles.
Problem 3 :
In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Find the value of 'x'.
Problem 4 :
In the figure given below, let the lines l1 and l2 be parallel and t is transversal. Find the value of 'x'.
1. Answer :
Vertically opposite angles are equal. | ∠1 = ∠3 ∠2 = ∠4 ∠5 = ∠7 ∠6 = ∠8 |
Corresponding angles are equal. | ∠1 = ∠5 ∠2 = ∠6 ∠3 = ∠7 ∠4 = ∠8 |
Alternate interior angles are equal. | ∠3 = ∠5 ∠4 = ∠6 |
Alternate exterior angles are equal. | ∠1 = ∠7 ∠2 = ∠8 |
Consecutive interior angles are supplementary. | ∠3 + ∠6 = 180° ∠4 + ∠5 = 180° |
Same side exterior angles are supplementary. | ∠1 + ∠8 = 180° ∠2 + ∠7 = 180° |
2. Answer :
From the given figure,
∠F and ∠H are vertically opposite angles and they are equal.
Then, ∠H = ∠F ----> ∠H = 65°.
∠H and ∠D are corresponding angles and they are equal.
Then, ∠D = ∠H ----> ∠D = 65.°
∠D and ∠B are vertically opposite angles and they are equal.
Then, ∠B = ∠D ----> ∠B = 65°.
∠F and ∠E are together form a straight angle.
Then, we have
∠F + ∠E = 180°
Substitute ∠F = 65°.
∠F + ∠E = 180°
65° + ∠E = 180°
∠E = 115°
∠E and ∠G are vertically opposite angles and they are equal.
Then, ∠G = ∠E ----> ∠G = 115°.
∠G and ∠C are corresponding angles and they are equal.
Then, ∠C = ∠G ----> ∠C = 115°.
∠C and ∠A are vertically opposite angles and they are equal.
Then, ∠A = ∠C ----> ∠A = 115°.
Therefore,
∠A = ∠C = ∠E = ∠G = 115°
∠B = ∠D = ∠F = ∠H = 65°
3. Answer :
From the given figure,
∠(2x + 20)° and ∠(3x - 10)° are corresponding angles.
So, they are equal.
Then, we have
2x + 20 = 3x - 10
30 = x
4. Answer :
From the given figure,
∠(3x + 20)° and ∠2x° are consecutive interior angles.
So, they are supplementary.
Then, we have
3x + 20 + 2x = 180
5x + 20 = 180
5x = 160
x = 32
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